Any device that relies on hiding secrets inside the silicon itself is subject to hacking. Several secure-enclave like chips have been hacked in the past by using electron microscopes and direct probes on the silicon. If BlackHat conference independent security researchers have the resources to pull this off, Apple and the NSA certainly can. Exfiltrating the Enclave UID could be done by various mechanisms at the chip level, especially if you have access to the actual HW design and can fab devices to help.
I mean, we're talking about threat models where chip-level doping has been shown as an attack. This just seems to be a variation on the same claims of copy protection tamper resistant dongles we've had forever. That someone builds a secure system that is premised on a secret being held in a tiny tamper-resistant piece, only the tamper resistance is eventually cracked.
It might even be the case that you don't even need to exfiltrate the UID from the Enclave, what the FBI needs to do is test a large number of PIN codes without triggering the backoff timer or wipe. But the wipe mechanism and backoff timer runs in the application processor, not on the enclave, and so it is succeptable to cracking attacks the same way much copy protection techniques are.
You may not need to crack the OS, or even upload a new firmware. You just need to disable the mechanism that wipes the device and delays how many wrong tries you get. So for example, if you can manage to corrupt, or patch the part of the system that does that, then you can try thousands of PINs without worrying about triggering the timer or wipe, and without needing to upload a whole new firmware.
I used to crack disk protection on the Commodore 64 and no matter how sophisticated the mechanism all I really needed to do was figure out one memory location to insert a NOP into, or change a BNE/BEQ branch destination, and I was done. Cracking often came down to mutating 1 or 2 bytes in the whole system.
(BTW, why the downvote? If you think I'm wrong, post a rebuttal)